Page 146 - Design and Operation of Heat Exchangers and their Networks

134 Design and operation of heat exchangers and their networks

The elements of the mn mn coefficient matrix A are given by Luo et al.
(2002) for both sequential and symmetrical block arrangements for i¼1, …,
n and j¼1, …, m as
U p, ij + η f, ij U f, ij

a i 1ð Þm + j, i 1Þm + j ¼ _
ð
C ij

1
1 p i 1ð Þm + j, i 1Þm + j + p Ii +1Þ 1Šm + j, i 1Þm + j
ð
½
ð
ð
2
(3.334)
U p, ij + η
f, ij U f, ij
a i 1ð Þm + j,l ¼ _ p i 1ð Þm + j,l + p Ii +1Þ 1Šm + j,l
½
ð
2C ij (3.335)
ð
ð l ¼ 1, …, mn; l 6¼ i 1Þm + jÞ
in which
α ij A f, ij
U f , ij ¼ (3.336)
L j
α ij A p, ij
U p, ij ¼ (3.337)
L j

1, i ¼ n + 1 and sequential arrangement
IiðÞ ¼ (3.338)
i, others
The fin efficiency η f is calculated by Eqs. (2.58), (2.59):
ð
tanh ml f =2Þ
η ¼ ð 2:58Þ, (3.339)
f
ml f =2
s ffiffiffiffiffiffiffiffiffiffiffiffi
αP
m ¼ ð 2:59Þ, (3.340)
λ f A c, f
In Eqs. (3.334), (3.335), p’s are the elements of the coefficient matrix of
plate temperatures P, with which the plate temperature vector T p can be
expressed as

T p xðÞ ¼ PT xðÞ (3.341)
The coefficient matrix P is the function of U f , U p , η f , and the fin bypass
efficiency μ f introduced by Haseler (1983), which is expressed as
2
μ ¼ (3.342)
f
ð ml f Þsinh ml f Þ
ð
The expressions of Q and C are different for different block arrangements.